How do you find the asymptotes for #f(x)= x/(x(x-2))#?
Vertical asymptotes, horizontal asymptotes and "holes" can be found in this function.
First, cancel the factor of x from both the numerator and denominator of the expression:
That factor being removed, causes a "hole" in the graph. This is sometimes called a removable discontinuity. So, at
To find a vertical asymptote, set the denominator equal to 0 and solve:
To find a horizontal asymptote, notice that the degree of x in the denominator is higher than the degree of x in the numerator. That is,
Still not sure about this? Substitute in large positive and negative values for x like 1000000 or -1000000...Your output values will be very, very small!